I would assume the majority of private servers are a result of either reverse engineering a game or, more likely, someone leaking it out.

Personally, I don't see the purpose in reverse engineering games. Play the games you like. If you're making a game, get a good engine and build the rest from that. Creativity is more fun than copying anyway.

There is purpose. Such as getting old games to work on modern computers, porting games on different operating systems or even different hardware. Translating games also often involves reverse engineering.